I'd like a new place to post them, but I'd like them to be better quality (at least 160 kbps, preferrably a little more), I'd like to be able to post them for free, and I'd like to be able to post more than the standard 3 free that I've seen around.

I don't play out. I don't have a cd. I'm not really interested in either of those things. I really just want a place where I can post new songs and let my friends on the other side of the country listen to them and tell me what to change.

In the alternative, any idea how much it would cost to just get a domain name and pay somebody to host a little site with 20 mp3's or more?

i think you'll just have to check out some host providers and find out what types of pricing plans are available. last time i checked, there were quite a few providers that had plans for around $5/month, and plenty of them for free.